STEP stats — 401 questions, 129 methods

Glossary

Curated question: — Past-paper question with a worked solution and a tagged method.
Method: — Portable technique that pops up across years.
Worked solution: — Step-by-step solution written by us in our voice.
Past paper: — Official exam session published by the board.

These pages only count the curated set: questions with both a worked solution and at least one tagged method. Bulk past papers without that treatment are hidden.

Method	2006	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	2024	2025
Limiting equilibrium: resolve in two directions, take moments, and impose $F = μ N$ at each contactMechanics	1			1		1	1	1			1	1	1	1		1	1	1	1
Treat the two horizontal coordinates of projectile motion separately, then eliminate the timeMechanics	1	1	1	1		1	1	1			1			1		1	1	1
Reduce a collision on a line to two scalars: conservation of momentum plus Newton's restitution ruleMechanics	2	1	1		1		1					1	1			1		1	1
Distribution of a transformed variable from the CDFProbability & Statistics			1			1		2	1		1		1	1	1	1
Condition on the first step to get a self-referential equationProbability & Statistics					1		1	2	1			1		1	2
Reflect the interval onto itself: $x \mapsto a + b - x$ , then add the two copiesIntegration	2			1					1	1		1		1		1
Telescope: write the general term as a difference $g (r) - g (r + 1)$ so the sum collapsesSequences & Series						2		1	1	1	1					1		1
Parametrise the conic, then run all tangent/normal/chord algebra in the parameterCoordinate Geometry & Conics	1	1						1			2	1				1
In "show that ... hence ...", the first part is the tool you must reuseProof & Number Theory		1	1				1			1			1	1			1
Count roots by sketching one side and sweeping a horizontal or moving line across itFunctions & Curve Sketching	1				1		2	1							1				1
Fold a tail onto a finite piece with $x \mapsto k / x$ (and exploit interval-preserving maps)Integration						1		1	1		1	1					1		1
Generate a reduction relation, then telescope or solve the recurrenceIntegration			1				1		1	1	1			1			1
Energy first for $v^{2}$ at a position, Newton along the normal for the reactionMechanics						1				1	1	1	1		2
Recognise the standard model, then approximate Binomial by Poisson or NormalProbability & Statistics	2									1			2				2
Affine-combination form of a line and the section formulaVectors & Matrices	1	1	1			1		1	1									1
Two points on a curve: carry $s + t$ and $s t$ (sum and product of parameters) as the variablesCoordinate Geometry & Conics			1							2	1						1	1
Exploit a kinematic constraint: differentiate the position relation to link velocities and accelerationsMechanics		1						1	1								2	1
Differentiate to convert acceleration: use $v d v / d x$ for speed-versus-position, $d v / d t$ for speed-versus-timeMechanics		1	2			1				1	1
Build a moment of inertia by composition, the parallel and perpendicular axis theorems, then use $I$ in rotational dynamicsMechanics	1	1				1	1		1			1
Variance of a sum through covariances and the bilinear expansionProbability & Statistics	2						1			2	1
Indicator variables plus linearity of expectationProbability & Statistics		2			1		1								1			1
Prove an inequality or an ordering by reading off the sign of a well-chosen derivativeDifferentiation	1										1	1	1					1
Rotation as multiplication: encode equilateral triangles and right angles by a fixed unimodular factorComplex Numbers	1	1						1			1			1
Reduce a chord/tangent/intersection condition to a quadratic and steer its discriminantCoordinate Geometry & Conics									1		1							2	1
Piecewise case-split at switch points for floor, modulus, and Min functionsFunctions & Curve Sketching	1							1								1			2

Glossary

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Questions per year

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Appendix — Year × method heatmap

Practice the methods that keep coming back.